Switching of the Spin-Density-Wave in CeCoIn$_5$ probed by Thermal Conductivity*

Unconventional superconductor CeCoIn$_5$ orders magnetically in a spin-density-wave (SDW) in the low-temperature and high-field corner of the superconducting phase. Recent neutron scattering experiment revealed that the single-domain SDW's ordering vector Q depends strongly on the direction of the magnetic field, switching sharply as the field is rotated through the anti-nodal direction. This switching may be manifestation of a pair-density-wave (PDW) $p$-wave order parameter, which develops in addition to the well-established $d$-wave order parameter due to the SDW formation. We have investigated the hypersensitivity of the magnetic domain with a thermal conductivity measurement. The heat current (J) was applied along the [110] direction such that the Q vector is either perpendicular or parallel to J, depending on the magnetic field direction. A discontinuous change of the thermal conductivity was observed when the magnetic field is rotated around the [100] direction within $0.2\,^{\circ}$. The thermal conductivity with the Q parallel to the heat current (J$\parallel$Q) is approximately 15\% lager than that with the Q perpendicular to the heat current (J$\perp$Q). This result is consistent with additional gapping of the nodal quasiparticle by the $p$-wave PDW coupled to SDW.